algebra with identity

algebra with identity

[¦al·jə·brə withi′den·ə·tē]
(mathematics)
An algebra which has an element, not equal to 0 and denoted by 1, such that, for any element x in the algebra, x 1 = 1 x = x.
References in periodicals archive ?
It is an associative algebra with identity given by the diagram corresponding to {{1, 1'}, .
In every Euclidean Jordan algebra with identity, the generic trace form, (x, y) [right arrow] tr(xy) is positive definite and associative.
Let V be a Euclidean Jordan algebra with identity e.
The linear space FL(V) is an algebra with identity I (the identity operator on Y), the multiplication being composition of operators.